AI Prediction and Constrained Energy Optimization of Industrial Thermal Systems Using Laplace Transform and RK4

Purpose: This study develops a hybrid framework that links data driven prediction with physically interpretable modelling and constrained energy optimization for industrial thermal systems such as furnaces, dryers, boilers, and ovens.
Research Methodology: A lumped thermal energy balance is formulated and analysed with the Laplace transform to obtain transfer functions, poles, and dominant time constants. A machine learning predictor estimates short horizon load disturbances or model residuals, the fourth order Runge Kutta (RK4) method propagates nonlinear trajectories for candidate control sequences, and a receding horizon optimizer balances energy cost, temperature tracking, and actuator movement under hard safety constraints.
Results: Illustrative synthetic simulations show that Laplace analysis and RK4 play complementary roles, that hard constraints must be separated from soft economic penalties, and that prediction accuracy alone is an inadequate criterion for deployment because uncertainty tails, infeasibility, and model mismatch determine operational safety.
Conclusions: Forecasting, physics based simulation, and constrained optimization should be evaluated as one decision pipeline, while each component retains its own validation evidence.
Limitations: The numerical examples are synthetic rather than measured plant results, the thermal model has a single state, and the AI layer is specified at the architecture level without training on industrial data.
Contributions: The paper clarifies the roles of each method, provides an explicit constraint hierarchy, and proposes a staged validation protocol covering chronological data splits, baseline comparison, uncertainty propagation, shadow mode testing, and operator supervised pilots.